A box of mass m1 = 10.0 kg rests on a smooth, horizontal floor next to a box of mass m2 = 5.0kg. You push on the box 1 with a horizontal force of F = 31.8 N:
a.)What net force on box 2 will cause it to have this acceleration?
b.)What the force on box 1 on box 2? (In other words, what is the contact force between the boxes?)
a force of 2on is applied a box of books with a mass of 4kg find the acceleration of the bo of books
To answer both parts of the question, we need to consider Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
a.) The net force on box 2 that will cause it to have the given acceleration can be calculated using the formula:
F = m * a
where F is the net force, m is the mass of an object, and a is its acceleration.
Given:
Mass of box 2 (m2) = 5.0 kg
Acceleration of box 2 (a) = to be determined
Since box 1 is pushed with a force of 31.8 N, we can assume that the force acting on box 2 is the same magnitude but opposite in direction. This is due to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
Therefore, the net force on box 2 can be calculated as:
F = m * a
31.8 N = 5.0 kg * a
Solving for a, we get:
a = 31.8 N / 5.0 kg
a ≈ 6.36 m/s²
So, the net force on box 2 that will cause it to have this acceleration is approximately 6.36 N.
b.) The force on box 2 due to box 1 can be calculated using the equation:
f = m * a
where f is the force and m is the mass of an object.
Given:
Mass of box 2 (m2) = 5.0 kg
Acceleration of box 2 (a) = 6.36 m/s²
Using the formula, we can determine the force on box 2:
f = m * a
f = 5.0 kg * 6.36 m/s²
f ≈ 31.8 N
So, the force exerted by box 1 on box 2 (also known as the contact force between the boxes) is approximately 31.8 N.
To find the answers to both parts of the question, we need to use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
a.) To determine the net force on box 2 that will cause it to have a specific acceleration, we first need to calculate the acceleration of box 1. Since the box is on a smooth, horizontal floor, there is no frictional force, so the only force acting on it is the force you exert, F.
Using Newton's second law: F = m1 ● a1
Rearranging the equation to solve for acceleration, we get: a1 = F / m1.
Substituting the given values, we have: a1 = 31.8 N / 10.0 kg = 3.18 m/s².
Now, we can determine the net force on box 2. The force on box 2 is the contact force between the boxes, and it has the same magnitude but opposite direction to the force on box 1.
Since the boxes are in contact and not slipping, the net force on box 2 is equal to the force exerted by box 1, F, and has the same direction.
Therefore, the net force on box 2 is 31.8 N in the same direction as the force you exerted.
b.) The force exerted by box 1 on box 2, which is the contact force between the boxes, is equal in magnitude but opposite in direction to the net force on box 2.
So, the force on box 1 on box 2 is 31.8 N in the opposite direction to the force you exerted.